What is the average speed of an object that is moving at #4 m/s# at #t=0# and accelerates at a rate of #a(t) =2-t# on #t in [0,3]#?

1 Answer
May 16, 2017

Answer:

#5.5 m/s#

Explanation:

I'm assuming this is related to one-dimensional motion. Combining the integral functions for velocity and position, the equation for position with respect to time is represented by

#x = x_0 + int_0^t [v_(0x) + int_0^ta_xdt]dt#

So, since the initial velocity #v_(0x) = 4 m/s#, the postion equation with respect to time from this is

#x = 4m/s(t) + 1m/(s^2)(t)^2 - 1/6m/(s^3)(t)^3#

and thus the position of the object at time #t = 3# is

#x = 4m/s(3) + 1m/(s^2)(3)^2 - 1/6m/(s^3)(3)^3 = 16.5m#

The average velocity on the interval #t in [0,3]# is thus

#v_(av-x) = (Deltax)/(Deltat) = (16.5m)/(3s) = 5.5 m/s #